I'm trying to redraw existing figures with TikZ as an exercise to learn it. This time I have choosen an interesting logo and I'm having difficulties drawing the arc. Here is the logo

I noticed that the red arc looks almost like an incomplete ellipse and found the interesting arc option in the manual. This may not be the best approach since the end of the arc (close to the last 'n') seems to deviate from the ellipse shape. Anyway, what I'm really interested is not the arc construction (I may file a separate question for that), but how I could draw the arc with varying line thickness. I.e. it starts very thin, and smoothly increases and decreases again.

Here's what I got so far (note: font is not right ... probably propriatary):